Solve sqrt{2}-sqrt{1/2}

$$\sqrt{ 2 } - \sqrt{ \frac{ 1 }{ 2 } }$$

Evaluate

$$\frac{\sqrt{2}}{2}\approx 0.707106781$$

Short Solution Steps

Rewrite the square root of the division \sqrt{\frac{1}{2}} as the division of square roots \frac{\sqrt{1}}{\sqrt{2}}.

$$\sqrt{2}-\frac{\sqrt{1}}{\sqrt{2}}$$

Calculate the square root of 1 and get 1.

$$\sqrt{2}-\frac{1}{\sqrt{2}}$$

Rationalize the denominator of \frac{1}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\sqrt{2}-\frac{\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\sqrt{2}-\frac{\sqrt{2}}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply \sqrt{2} times \frac{2}{2}.

$$\frac{2\sqrt{2}}{2}-\frac{\sqrt{2}}{2}$$

Since \frac{2\sqrt{2}}{2} and \frac{\sqrt{2}}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\sqrt{2}-\sqrt{2}}{2}$$

Do the calculations in 2\sqrt{2}-\sqrt{2}.

$$\frac{\sqrt{2}}{2}$$